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In the face of increasingly clear climate-change impacts and continued inadequacy of efforts to reduce greenhouse-gas emissions and adapt to ongoing climate changes, increasing attention has been directed to geoengineering: deliberate large-scale interventions in the Earth’s climate system to moderate global warming. Such interventions could reduce risks in novel ways, but are controversial because they present an uncertain, high-stakes mix of potential benefits and risks. Solar geoengineering poses especially acute international governance needs, particularly in the case of potential future demands to use it. Many aspects of geoengineering present deep, ill-structured uncertainties that carry high stakes for near-term decisions, and are thus suitable for exploration through scenarios. This collection of papers reports on a major scenario exercise examining governance challenges and potential responses for solar geoengineering, held at the International Summer School on Geoengineering Governance in Banff, Canada in 2019. This opening paper introduces geoengineering and the concerns it raises, particularly as they pertain to governance; reviews the design and use of scenario exercises to inform decisions under uncertainty, including their prior uses related to climate change and geoengineering; and outlines the aims, design, and process of this scenario exercise.